Since there is currently no way and/or need for Jews to administer capital punishment to gentiles who violate the 7 noahide laws, is there any halachic reason for a Jew to care whether or not a non-Jew engages in homosexuality?

I am asking if there is any halachic basis to mandate that a Jew care (if you prefer 'actively object') about non-Jewish homosexuality today. If no such mandate exists, that does not necessarily mean the inverse is true (i.e. that you may actively accommodate this behavior).

To be clear, this is not related to chinuch or the desire not to be exposed and influenced by practices that are antithetical to the torah. I am asking this in a purely halachic context.

1 Answer
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Rambam writes in Hilchos Melachim 8:10 that Moshe Rabeinu commanded us to force all humans to follow the 7 Mitzvos (and if they refuse, we must execute them).

It is quite clear that in our times we don't have the power to enforce the penalty, but that doesn't mean that we are less obligated in trying to convince all people to follow the 7 Mitzvos voluntarily.

Some would argue that this obligates Jews to actively promote observance of the 7 laws among gentiles. Others would argue that although this is theoretically true, as a matter of priorities we should expend such energies on Jewish outreach first. But I can't imagine a justification for "not caring". It is quite clear that G-d cares so obviously we should care.

Snow crab legs are sold in supermrkets and are sometimes taken from live snow crabs. There are houses of worship of idolatrous religions. No one seems to get terribly upset about these things. Why should we yell and scream about one and not the other?
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Ze'ev FelsenNov 12 '12 at 20:44

snow crab legs are taken from live snow crabs?
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Jim ThioMar 28 '13 at 4:00

@AaronShaffier - Your quotation of the Rambam is out of context. Notice that it is found in Hil. Melakhim Umilhhamoth. This means (and the direct surrounding context dictates) that we are not to "force" all humans to follow the Sheva` Misswoth Benei Noahh. Instead, any non-Jewish person who desires to dwell among the Jewish people in their Land as ger toshav needs to be compelled to strictly follow the misswoth that apply to him under penalty of death at the hands of the Jewish court where he dwells.
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MaimonistJul 5 at 18:27

@AaronShaffier - You do not EVER see ANY of the Hakhmei Bavel - or even the hakhamim of Eress Yisra'el - forcing all non-Jews around them to follow the Sheva` Misswoth. This is because the non-Jews around them were not dwelling in the land under Jewish jurisprudence with the permission of Jewish courts as gerei toshav. These types of generalizations make Judaism look like a "convert or die" religion of the sword, which it is certainly not. All that the halakhah requires is that those who want to live in EY without converting submit themselves strictly to the universal laws. Kol tuv
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MaimonistJul 5 at 18:32